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1.
Bangming Deng 《Proceedings of the American Mathematical Society》1996,124(6):1673-1677
Let be an artin algebra. This paper presents a sufficient condition for the subcategory of to be contravariantly finite in , where is the subcategory of consisting of --modules of projective dimension less than or equal to . As an application of this condition it is shown that is contravariantly finite in for each when is stably equivalent to a hereditary algebra.
2.
William T. Ross 《Proceedings of the American Mathematical Society》1996,124(6):1841-1846
In this paper, we comment on the complexity of the invariant subspaces (under the bilateral Dirichlet shift ) of the harmonic Dirichlet space . Using the sampling theory of Seip and some work on invariant subspaces of Bergman spaces, we will give examples of invariant subspaces with , . We will also generalize this to the Dirichlet classes , , as well as the Besov classes , , .
3.
Athanassios G. Kartsatos 《Proceedings of the American Mathematical Society》1996,124(6):1811-1820
Let be a real Banach space. Let be -accretive with compact. Let be such that is condensing for some Let and assume that there exists a bounded open set and such that is bounded and
for all Then A basic homotopy result of the degree theory for with condensing and possibly unbounded, is used to improve and/or extend recent results by Hirano and Kalinde.
4.
We prove that if a commutative semi-simple Banach algebra is the range of a ring homomorphism from a commutative -algebra, then is -equivalent, i.e. there are a commutative -algebra and a bicontinuous algebra isomorphism between and . In particular, it is shown that the group algebras , and the disc algebra are not ring homomorphic images of -algebras.
5.
Alan K. Kingsbury Rodney Y. Sharp 《Proceedings of the American Mathematical Society》1996,124(6):1703-1711
Let be ideals of the commutative ring , let be a Noetherian -module and let be a submodule of ; also let be an Artinian -module and let be a submodule of . It is shown that, whenever is a sequence of -tuples of non-negative integers which is non-decreasing in the sense that for all and all , then Ass is independent of for all large , and also Att is independent of for all large . These results are proved without any regularity conditions on the ideals , and so (a special case of) the first answers in the affirmative a question raised by S. McAdam.
6.
Alexander R. Pruss 《Proceedings of the American Mathematical Society》1996,124(6):1755-1761
We construct domains in the plane such that if is the Green's function of with pole at zero, while is the symmetric non-increasing rearrangement of for each fixed and is the Green's function of the circular symmetrization , again with pole at zero, then there are positive numbers and such that
whenever . One of our constructions will have simply connected. We also consider the case where the poles of the Green's functions do not lie at the origin. Our work provides a negative answer to a question of Hayman (1967).
7.
The notion of (strongly) hereditarily aspherical compacta introduced by Daverman (1991) is modified. The main results are: Theorem. If is a hereditarily aspherical compactum, then ANR. In particular, is strongly hereditarily aspherical. Theorem. Suppose is a cell-like map of compacta and is shape aspherical for each closed subset of . Then
- 1.
- Y is hereditarily shape aspherical,
- 2.
- is a hereditary shape equivalence,
- 3.
- .
- 1.
- and ,
- 2.
- .
8.
Let and be real Banach spaces. A map between and is called an -bi-Lipschitz map if for all . In this note we show that if is an -bi-Lipschitz map with from onto , then is almost linear. We also show that if is a surjective -bi-Lipschitz map with , then there exists a linear isomorphism such that
where as and .
9.
Let be a locally compact group equipped with right Haar measure. The right differences of functions on are defined by for . Let and suppose for some and all . We prove that is a right uniformly continuous function of . If is abelian and the Beurling spectrum does not contain the unit of the dual group , then we show . These results have analogues for functions , where is a separable or reflexive Banach space. Finally, we apply our methods to vector-valued right uniformly continuous differences and to absolutely continuous elements of left Banach -modules.
10.
Kang Zhao 《Proceedings of the American Mathematical Society》1996,124(6):1857-1867
After exploring some topological properties of locally finite-dimensional shift-invariant subspaces of , we show that if provides approximation order , then it provides the corresponding simultaneous approximation order. In the case is generated by a compactly supported function in , it is proved that provides approximation order in the -norm with if and only if the generator is a derivative of a compactly supported function that satisfies the Strang-Fix conditions.
11.
Jon F. Carlson Hans-Werner Henn 《Proceedings of the American Mathematical Society》1996,124(3):665-670
Suppose that is a compact Lie group or a discrete group of finite virtual cohomological dimension and that is a field of characteristic . Suppose that is a set of elementary abelian -subgroups such that the cohomology is detected on the centralizers of the elements of . Assume also that is closed under conjugation and that is in whenever some subgroup of is in . Then there exists a regular element in the cohomology ring such that the restriction of to an elementary abelian -subgroup is not nilpotent if and only if is in . The converse of the result is a theorem of Lannes, Schwartz and the second author. The results have several implications for the depth and associated primes of the cohomology rings.
12.
P. D. Johnson Jr. R. N. Mohapatra Jr. David Ross Jr. 《Proceedings of the American Mathematical Society》1996,124(2):543-547
Suppose is a non-increasing sequence of non-negative numbers with , , , and is the lower triangular matrix defined by , , and , . We show that the operator norm of as a linear operator on is no greater than , for ; this generalizes, yet again, Hardy's inequality for sequences, and simplifies and improves, in this special case, more generally applicable results of D. Borwein, Cass, and Kratz. When the tend to a positive limit, the operator norm of on is exactly . We also give some cases when the operator norm of on is less than .
13.
F. Thaine 《Proceedings of the American Mathematical Society》1996,124(1):35-45
Let be a prime number, a -th primitive root of 1 and the periods of degree of . Write with . Several characterizations of the numbers and (or, equivalently, of the cyclotomic numbers of order ) are given in terms of systems of equations they satisfy and a condition on the linear independence, over , of the or on the irreducibility, over , of the characteristic polynomial of the matrix .
14.
Ludomir Newelski 《Proceedings of the American Mathematical Society》1996,124(8):2519-2525
Assume is superstable, is a formula over , is countable and is countable and . We investigate models in assuming has the prime model property. We prove some corollaries on the number of models in . We show an example of an -stable and with having exactly 3 models.
15.
A probability measure on a product space is said to be bistochastic with respect to measures on and on if the marginals and are exactly and . A solution is presented to a problem of Arveson about sets which are of measure zero for all such .
16.
Katsuo Chiba 《Proceedings of the American Mathematical Society》1996,124(6):1649-1653
Let be a skew field with infinite center such that , and let be a non-central subnormal subgroup of the multiplicative group of . Then there are no non-trivial generalized rational identities of . This generalizes a theorem proved by Makar-Limanov.
17.
Kazuyuki Enomoto Yoshihisa Kitagawa Joel L. Weiner 《Proceedings of the American Mathematical Society》1996,124(1):265-268
Let be the unit hypersphere in the 4-dimensional Euclidean space defined by . For each with , we denote by the Clifford torus in given by the equations and . The Clifford torus is a flat Riemannian manifold equipped with the metric induced by the inclusion map . In this note we prove the following rigidity theorem: If is an isometric embedding, then there exists an isometry of such that . We also show no flat torus with the intrinsic diameter is embeddable in except for a Clifford torus.
18.
For a separable infinite-dimensional Hilbert space , we consider the full algebra of bounded linear transformations and the unique non-trivial norm-closed two-sided ideal of compact operators . We also consider the quotient -algebra with quotient map
For any -subalgebra of , the relative commutant is given by for all in . It was shown by D. Voiculescu that, for any separable unital -subalgebra of ,
In this note, we exhibit a non-separable unital -subalgebra of for which (VDCT) fails.
19.
Stephen J. Gardiner 《Proceedings of the American Mathematical Society》1996,124(4):1149-1157
Let , where is polar and compact and is a domain with Green function . We characterize those subsets of which have the following property: Every positive continuous function on can be written as , where and for each .
20.
Zoran Spasojevic 《Proceedings of the American Mathematical Society》1996,124(12):3857-3865
For a partial order , let denote the statement that for every -increasing -sequence there is a -decreasing -sequence on top of such that is an -gap in . The main result of this paper is that . It is also shown, as a corollary, that but .